A little aluminum boat (mass of 14.50g) has a volume of 450.00cm3. The boat is placed in a small pool of water and carefully filled with pennies. If each penny has a mass of 2.50g, how many pennies can be added to the boat before it sinks?

you cant have .2 pennies,so it sinks on the 175th penny.

the boat will displace its mass in water or 450 gm...what does this line mean? could you please explain

Well, I must say this is quite the aquatic riddle! Let's dive in.

To determine how many pennies the boat can hold before it takes a nosedive, we need to calculate the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the boat.

The weight of an object can be calculated by multiplying the mass of the object by gravity (which is approximately 9.8 m/s²). In this case, the weight of the boat is 14.50g * 9.8 m/s².

Now, to find out how many pennies the boat can hold, we need to compare the weight of the boat to the weight of the pennies added. One penny weighs 2.50g, so we can divide the weight of the boat by the weight of one penny to find the number of pennies.

However, we are given the volume of the boat (450.00cm³), not its weight. So, we need to assume that the density of the boat is the same as that of water, which is approximately 1g/cm³. Thus, the mass of the boat is equal to its volume multiplied by its density.

Plugging the values into our buoyancy equation, we can determine the maximum number of pennies that can be added before the boat goes kaput. But remember, my dear friend, that this calculation assumes ideal conditions, and real-life situations can sometimes be trickier than an octopus playing hide-and-seek.

So, let's calculate the answer and find out the boat's financial limits!

To determine how many pennies can be added to the boat before it sinks, we need to compare the total mass of the boat to the buoyant force exerted by the water.

First, let's determine the mass of the aluminum boat. The mass is given as 14.50g.

Next, we need to find the mass of the water displaced by the boat. The volume of the boat is given as 450.00cm^3, which is equivalent to 450.00g of water. This is because 1cm^3 of water has a mass of 1g.

So, the mass of the water displaced by the boat is 450.00g.

Now, let's calculate the buoyant force exerted by the water on the boat. The buoyant force is equal to the weight of the water displaced. The weight of an object can be calculated using the formula:

Weight = mass x gravity

The gravity is constant and typically taken as 9.8m/s^2. However, since we're working with grams and centimeters, we'll use 9.8cm/s^2.

The weight of the water displaced by the boat can be calculated as:

Weight of water displaced = mass of water displaced x gravity

Substituting the values, we get:

Weight of water displaced = 450.00g x 9.8cm/s^2

Now we have the buoyant force exerted by the water on the boat.

To determine if the boat will sink, we compare the total mass of the boat (14.50g) to the buoyant force exerted by the water. If the total mass is greater than the buoyant force, the boat will sink.

Now, we need to calculate how many pennies can be added to the boat to reach the sinking point.

Each penny is given a mass of 2.50g. So, to calculate the number of pennies, we divide the difference between the total mass of the boat and the buoyant force by the mass of a single penny.

Number of pennies = (Total mass of boat - Buoyant force) / Mass of a penny

Substituting the values, we get:

Number of pennies = (14.50g - Weight of water displaced) / 2.50g

By plugging in the values and calculating the expression, you can determine the number of pennies that can be added to the boat before it sinks.

The boat will displace its mass in water, or 450 grams

n*2.5 + 14.5=450
solve for n.

n=174.2 right?

How can you do that?

ThIs Is tHe Wort=St QueStiOn EverR